CN114310877A - Robot Collaborative System and Its Application and Machining Accuracy Evaluation Method - Google Patents

Abstract

Translated fromChinese

本发明提供了一种机器人协同系统及其应用和加工精度评价方法，使用工件的基准作为全域坐标，并据此对每个机器人建立对应的运动方程，实际上是建立了以工件为恒星，多个加工机器人为行星的多机器人协同系统，从而使得整个多机器人协同系统的每个机器人都通过工件的基准建立相应的联系，以满足对复杂的不规则工件加工的需要，解决了传统需要将工件在不同加工设备之间转移以达至完成不同加工工序，因只需系统进行一次性的定位并建立基准即可完成全部的加工，可减少工件转移时需要不断更换基准所导致的繁复操作以及产生的安装误差，能够缩短加工时间，降低制造成本，同时提供工件加工的精度。

The invention provides a robot collaborative system and its application and processing accuracy evaluation method. The reference of the workpiece is used as the global coordinate, and a corresponding motion equation is established for each robot accordingly. One processing robot is a planetary multi-robot collaborative system, so that each robot in the entire multi-robot collaborative system establishes a corresponding connection through the workpiece benchmark, so as to meet the needs of complex irregular workpiece processing, and solve the traditional need to Transfer between different processing equipment to complete different processing procedures, because the system only needs to perform one-time positioning and establish a reference to complete all processing, which can reduce the complicated operation and production caused by the need to constantly replace the reference when the workpiece is transferred. The installation error can be shortened, the processing time can be shortened, the manufacturing cost can be reduced, and the accuracy of workpiece processing can be improved.

Description

Translated fromChinese

机器人协同系统及其应用和加工精度评价方法Robot Collaborative System and Its Application and Machining Accuracy Evaluation Method

技术领域technical field

本发明专利涉及一种多机械人的协同加工系统，尤其是一种采用处理对象的基准作为全域坐标系对所有机器人建立运动模型实现协同加工的系统。The patent of the present invention relates to a multi-robot collaborative processing system, especially a system that uses the reference of the processing object as the global coordinate system to establish motion models for all robots to realize collaborative processing.

背景技术Background technique

在过去的几十年中，增材制造（AM）是重大变革的制造技术之一。快速成型和技术创新不断增长的需求推动了增材制造的发展。为了适应生物技术，材料科学，航空航天和医学中预期的多种应用，已经取得了巨大的进步。对于金属材料而言，最为普遍的的增材制造技术是粉末冶金和金属沉积。在过去的十年中，混合制造逐步发展，整合了增材制造和减材制造，以改善获得产品的整体质量及精度。制造时需要对工件进行固定并设定加工基准，通常是使用底板来提供基准坐标，但是由于底板的重复使用成本高昂，因此效果较差。Additive Manufacturing (AM) has been one of the major transformational manufacturing technologies in the past few decades. The growing demand for rapid prototyping and technological innovation has driven the development of additive manufacturing. Huge progress has been made to accommodate the multiple applications expected in biotechnology, materials science, aerospace and medicine. For metallic materials, the most common additive manufacturing techniques are powder metallurgy and metal deposition. Over the past decade, hybrid manufacturing has evolved to integrate additive and subtractive manufacturing to improve the overall quality and precision of the resulting product. During manufacture, it is necessary to fix the workpiece and set the machining datum. Usually, the base plate is used to provide the reference coordinates, but the effect is poor due to the high cost of repeated use of the base plate.

用于增材制造的产品设计可以形成复杂形状和结构。可以对每个原型和产品采用定制设计，而不会增加制造成本。当增材制造的引入医疗产品，促进了定制的发展。定制的医疗产品通常是针对特定患者的，旨在模仿生物功能和生物力学，例如密度，孔隙率，表面粗糙度和生物相容性。尤其人体骨胳，是一个复杂的系统，由大约200多个骨胳组成。特别是关节部分的骨头几何形状复杂。在借助3D成像和CT扫描的获取骨胳的数据已经取得了许多进展。这些技术的发展使得现代的人造植入物能够有效模仿人体解剖结构，并增加了兼容性并改善了患者的体验。以便带来良好的临床效果，例如更好的患者依从性和更高的疗效等等。Product designs for additive manufacturing can form complex shapes and structures. Custom designs can be applied to each prototype and product without increasing manufacturing costs. When additive manufacturing was introduced into medical products, it facilitated the development of customization. Customized medical products are often patient-specific and designed to mimic biological functions and biomechanics such as density, porosity, surface roughness, and biocompatibility. The human skeleton, in particular, is a complex system consisting of about 200 bones. In particular, the bone geometry of the joint part is complex. Much progress has been made in obtaining bone data with the aid of 3D imaging and CT scans. The development of these technologies has allowed modern artificial implants to effectively mimic human anatomy, increasing compatibility and improving the patient experience. In order to bring good clinical results, such as better patient compliance and higher efficacy and so on.

医疗用的植入物，通常需要使用各种不同的加工设备，制造过程例如包括线切割，热处理，机加工，抛光，雕刻，涂层，清洁和消毒等等。鉴于定制医疗产品相比标准化产品更加复杂，需要重新审视定制医疗产品的制造过程。传统的金属加工工艺已经很成熟，但通常倾向于大规模生产应用。通过重复的反复试验和操作，保证了准确性，公差和可重复性即可达至使用要求。但是，定制产品的制造不能遵循相同的程序，因为定制产品之间存在较大的差异。为了寻求可灵活及更为广泛的制造平台。需要使用具有内置参考基准设置的多机器人系统（Muli-robot System ，即MRS），以解决缺乏针对定制产品的金属加工的工业化解决方案。Implants for medical use usually require the use of a variety of processing equipment, such as wire cutting, heat treatment, machining, polishing, engraving, coating, cleaning and sterilization. Given that custom medical products are more complex than standardized products, the manufacturing process of custom medical products needs to be revisited. Traditional metalworking processes are well established, but generally lean towards mass production applications. Through repeated trial and error and operation, the accuracy, tolerance and repeatability are guaranteed to meet the requirements of use. However, the manufacture of customized products cannot follow the same procedure because there are large differences between customized products. In order to seek a flexible and broader manufacturing platform. A multi-robot system (Muli-robot System, or MRS) with a built-in reference datum setup is required to address the lack of industrialized solutions for metalworking of custom products.

为使MRS的各个机器人之间能够相互配合完成整个加工过程，需要对其建立运动学模型，目前主要基于三种运动学模型：i）基于行为的设计方法（behavior-basedmethod）； ii）虚拟结构方法（virtual structure method）； iii）Leader-follower方法。In order to enable each robot of MRS to cooperate with each other to complete the entire processing process, it is necessary to establish a kinematic model for it. At present, three kinematic models are mainly based: i) behavior-based design method; ii) virtual structure method (virtual structure method); iii) Leader-follower method.

基于行为的方法通过彼此共享机器人的姿势来提供清晰的信息反馈，并将结构控制转化为每个机器人的一系列基本行为。此方法无法建立特定的数学模型来分析整个过程，因为它没有提供任何有关群体行为的数学定义。Behavior-based methods provide clear feedback of information by sharing robot poses with each other and translate structural control into a set of basic behaviors for each robot. This method cannot establish a specific mathematical model to analyze the whole process, because it does not provide any mathematical definition of group behavior.

虚拟结构方法是基于被视为虚拟刚性结构的地层构建的。组中的每个机器人将保持相同的相对位置。The virtual structure method is constructed based on strata that are considered as virtual rigid structures. Each robot in the group will maintain the same relative position.

使用Leader-follower方法时，机器人充当“Leader”，而其他机器人充当“Follower”。 Leader与Follower之间的距离，相对角度是主要参数。When using the Leader-follower method, the robot acts as a "Leader" and other robots act as "Followers". The distance between Leader and Follower, the relative angle is the main parameter.

以上三种方法都与机器人之间的关系有关。没有有关机器人与要生产/维修的零件之间的几何关系的信息。在用于制造/维修的MRS中，机器人与产品之间的几何关系至关重要。机器人根据产品规格生成工具路径以生产产品。The above three methods are all related to the relationship between robots. There is no information about the geometry between the robot and the part to be produced/repaired. In MRS for manufacturing/maintenance, the geometric relationship between robot and product is critical. Robots generate tool paths based on product specifications to produce products.

发明内容SUMMARY OF THE INVENTION

针对上述现有技术的不足，本发明提供了一种用于实现不规则加工的多机器人协同系统，将整个系统的基准设置于处理对象上，并以该基准建立全域坐标系，以便成为系统中每个活动机器人的参考点，以在每个一个后处理步骤中能够相对于工件重新准确定位的几何坐标，即使机器人的相应基板产生的变形而导致定位信息丢失，机械人仍可以跟踪处理对象的几何坐标，实现多机器人协同对处理对象进行加工。Aiming at the above-mentioned deficiencies of the prior art, the present invention provides a multi-robot collaborative system for realizing irregular processing. The benchmark of the entire system is set on the processing object, and the global coordinate system is established based on the benchmark, so as to become the center of the system. The reference point of each active robot, with geometric coordinates that can be accurately repositioned relative to the workpiece in each post-processing step, even if the corresponding substrate of the robot is deformed and the positioning information is lost, the robot can still track the processing object. Geometric coordinates to realize multi-robot collaborative processing of processing objects.

而且，本发明还提供了一种利用多机器人协同系统对不规则工件进行加工的方法，能够通过机器人建立协同的加工模型实现对不规则工件进行机械加工，以制造十分复杂形状的医疗产品，并能够缩短加工时间，降低制造成本。Moreover, the present invention also provides a method for processing irregular workpieces by using a multi-robot collaborative system, which can realize mechanical processing of irregular workpieces by establishing a collaborative processing model with robots, so as to manufacture medical products with very complex shapes, and The processing time can be shortened and the manufacturing cost can be reduced.

另外，本发明还提供了用于对多机械人协同系统的精度评价方法，以便用户能够方便地实现对多机械人协同系统的整体精度进行调校及评价。In addition, the present invention also provides a method for evaluating the accuracy of the multi-robot collaborative system, so that the user can easily adjust and evaluate the overall accuracy of the multi-robot collaborative system.

本发明通过以下技术方案实现：The present invention is achieved through the following technical solutions:

多机器人协同系统，包括待处理的对象以及围绕是设置于处理对象周围的多个的机器人，机械人上设置相应的处理器械；处理对象设置有基准，处理器械以该基准为全域坐标系对其运动进行运动建模，具体为：A multi-robot collaborative system includes an object to be processed and a plurality of robots arranged around the object to be processed, and corresponding processing equipment is set on the robot; Motion performs motion modeling, specifically:

a.机械人i具有M_i个运动自由度；以机械人i的内建坐标系，安装于机器人i上的第j关节建立以下齐次变换方程：a. Robot i has M_i degrees of freedom of movement; with the built-in coordinate system of robot i, the jth joint installed on robot i establishes the following homogeneous transformation equation:

A_i,j= Rotz(θ_i,j)Tansz(d_i,j)Transx(a_i,j)Rotx(α_i,j)=A_i,j = Rotz(θ_i,j) Tansz(d_i,j )Transx(a_i,j )Rotx(α_i,j )=

……(1)

……(1)

上式中i、j及M_i为自然数，

、

、

及

分别为机械臂扭角，机械臂长度，机械臂偏移距离和机械臂夹角；In the above formula, i, j and M_i are natural numbers,

,

,

and

are the torsion angle of the manipulator, the length of the manipulator, the offset distance of the manipulator and the included angle of the manipulator;

从而获得安装于机械人i上处理器械的运动方程为：Thus, the equation of motion of the processing instrument installed on the robot i is obtained as:

……(2)

……(2)

b.机器人i的安装基座I的基座坐标系与全域坐标系的位置关系建立,以下其次变换方程：b. The positional relationship between the base coordinate system of the installation base I of the robot i and the global coordinate system is established, and the following transformation equation is followed:

A_i,F=

……(3)A_i,F=

...(3)

上式中i为自然数，F为机器人i中的某个关节，

、

、

及

分别为某关节F相对于全域坐标系的扭角，长度，偏移距离和夹角；In the above formula, i is a natural number, F is a joint in robot i,

,

,

and

are the torsion angle, length, offset distance and included angle of a joint F relative to the global coordinate system;

c.根据机器人i的内建坐标系与安装基座的基座坐标系的位置关系建立以下齐次变换方程：c. Establish the following homogeneous transformation equation according to the positional relationship between the built-in coordinate system of robot i and the base coordinate system of the installation base:

A_i,I=

……(4)A_i,I=

...(4)

上式中分别i，I为自然数，，

、

、

及

为安装基座I相对于全局坐标系的扭角、长度、偏移距离和夹角；In the above formula, i and I are natural numbers, respectively,

,

,

and

is the torsion angle, length, offset distance and included angle of the mounting base I relative to the global coordinate system;

d.获得于机械人i上处理器械的相对于全域坐标的运动方程为：d. The motion equation relative to the global coordinates of the processing instrument obtained on the robot i is:

……(5)

...(5)

其中，所述锁定装置包括用螺丝锁定于刚性底座上的刚性调整滑轨。Wherein, the locking device includes a rigid adjusting slide rail locked on the rigid base with screws.

其中，所述机器人还包括用于固定处理对象的夹持机械人,所述处理对象夹持固定于设置于机器人上的夹持座上。Wherein, the robot further includes a clamping robot for fixing the processing object, and the processing object is clamped and fixed on a clamping seat provided on the robot.

将多机器人协同系统应用于对不规则工件进行加工的方法，所述机器人包括切削机械人、工件夹持机械人以及冷却机械人，将不规则的待加工工件安装于工件夹持机器人的固定座上，切削机器人上安装有用于对工件进行加工的刀具，冷却机械人设有对工件进行冷却的冷却剂喷射装置；首先将工件的坐标系设定为全域坐标系，然后根据各个机器人的自有坐标与全域坐标系之间的位置关系建立相应的运动方程，通过工件的加工轮廓生成加工刀路，各个机械人分别依照加工刀路以及其相应的运动方程计算获得各机器人自有的加工路线，由相应的机器人控制分别控制刀具，夹持工件的固定座以及冷却剂喷射装置完成对待加工工件的所有加工工序。A method of applying a multi-robot collaborative system to processing irregular workpieces, the robot includes a cutting robot, a workpiece clamping robot and a cooling robot, and the irregular workpiece to be processed is installed on the fixed seat of the workpiece clamping robot The cutting robot is equipped with a tool for processing the workpiece, and the cooling robot is equipped with a coolant injection device for cooling the workpiece; first, the coordinate system of the workpiece is set as the global coordinate system, and then according to the individual robot's own The positional relationship between the coordinates and the global coordinate system establishes the corresponding motion equation, and generates the machining tool path through the machining contour of the workpiece. Each robot calculates and obtains its own machining path according to the machining tool path and its corresponding motion equation. The corresponding robot control controls the tool, the fixed seat holding the workpiece and the coolant injection device to complete all the processing procedures of the workpiece to be processed.

其中，所述工件的基准为在工件或底座表面通过三维打印形成的基准柱，以基准柱设置工件的坐标系。Wherein, the reference of the workpiece is a reference column formed by three-dimensional printing on the surface of the workpiece or the base, and the reference column is used to set the coordinate system of the workpiece.

其中，还设有有三维扫描仪，三维扫描仪对待加工工件进行实时扫描以获得待加工工件的测量尺寸，并将测量尺寸与工件的加工轮廓数据进行对比，如测量尺寸超出设定的加工误差，切削机械人根据加工误差控制刀具对待加工工件进行加工。Among them, there is also a three-dimensional scanner. The three-dimensional scanner scans the workpiece to be processed in real time to obtain the measured size of the workpiece to be processed, and compares the measured size with the processing contour data of the workpiece. If the measured size exceeds the set processing error , the cutting robot controls the tool to process the workpiece to be processed according to the processing error.

其中，还包括对机器人复位的如下工作步骤：Among them, it also includes the following working steps for resetting the robot:

i.将标准的球形校准工件安装至工件夹持机械人上,将复位校准用的探针安装至切削机械人上；i. Install the standard spherical calibration workpiece on the workpiece clamping robot, and install the probe for reset calibration on the cutting robot;

ii.切削机器人驱动探针与球形校准工件的不同位置接触，并获得多个接触点坐标，通过接触点坐标拟合计算球形校准工件的球心坐标；ii. The cutting robot drives the probe to contact different positions of the spherical calibration workpiece, and obtains multiple contact point coordinates, and calculates the spherical center coordinates of the spherical calibration workpiece by fitting the contact point coordinates;

iii．将球心坐标记录并简练以球心坐标为原点，X、Y及Z为方向向量的全域坐标系。iii. Record and succinctly take the spherical center coordinates as the origin, and X, Y and Z as the direction vectors of the global coordinate system.

对多机器人协同系统的加工精度评价方法，首先建立一个标准模型，该标准模型包括球体、圆柱体、参考圆柱体和基础块，将该标准模型作为工件安装于多机器人协同系统中，机器人按照标准模型设定的加工量，加工刀路及对应的运动方程计算获得机器人的自有加工路线，并对标准模型的球体、圆柱体以及基础块进行加工，获得加工后的标准模型，最后对加工后的标准模型的尺寸进行度量，将度量获得的数据与标准模型设定的加工量进行比对获得多机器人协同系统的加工精度。For the evaluation method of the machining accuracy of the multi-robot collaborative system, a standard model is first established, which includes a sphere, a cylinder, a reference cylinder and a base block. The standard model is installed as a workpiece in the multi-robot collaborative system. The processing amount set by the model, the processing tool path and the corresponding motion equation are calculated to obtain the robot's own processing route, and the sphere, cylinder and basic block of the standard model are processed to obtain the processed standard model. The size of the standard model is measured, and the data obtained by the measurement is compared with the processing amount set by the standard model to obtain the processing accuracy of the multi-robot collaborative system.

本发明的有益效果：使用处理对象的基准作为全域坐标，并据此对每个机器人建立对应的运动方程，实际上是建立了以处理对象为恒星，安装基座为行星及多个加工机器人为卫星的多机器人协同系统，从而使得整个多机器人协同系统的每个机器人都通过处理对象的基准建立相应的联系，以满足对复杂的不规则对象加工的需要，解决了传统需要将对象在不同加工设备之间转移以达至完成不同加工工序，因只需系统进行一次性的定位并建立基准即可完成全部的加工，可减少对象转移时需要不断更换基准所导致的繁复操作以及产生的安装误差，能够缩短加工时间，降低制造成本，同时提供对讲加工的精度。本系统个可广泛应用于不规则产品的制造中，甚至可应用于以人体作为处理对象的医疗手术中。The beneficial effects of the present invention are as follows: using the reference of the processing object as the global coordinate, and establishing the corresponding motion equation for each robot accordingly, in fact, the processing object is a star, the installation base is a planet, and a plurality of processing robots are The satellite-based multi-robot collaborative system enables each robot in the entire multi-robot collaborative system to establish a corresponding connection through the reference of the processing object, so as to meet the needs of complex irregular object processing, and solve the traditional need to process objects in different processing. Transfer between devices to complete different processing procedures, because the system only needs to perform one-time positioning and establish a reference to complete all processing, which can reduce the complicated operation and installation errors caused by the need to constantly replace the reference when the object is transferred. , which can shorten the processing time, reduce the manufacturing cost, and provide the precision of the intercom processing. The system can be widely used in the manufacture of irregular products, and even in medical operations that take the human body as the object of treatment.

附图说明Description of drawings

下面结合附图对本发明进一步说明：Below in conjunction with accompanying drawing, the present invention is further described:

图1是本发明的立体图；Fig. 1 is the perspective view of the present invention;

图2是使用增材制造方法制造的定制医疗产品示意图；Figure 2 is a schematic diagram of a custom medical product manufactured using an additive manufacturing method;

图3是本发明的全局坐标系与机械人坐标系的平面示意图；Fig. 3 is the plane schematic diagram of the global coordinate system of the present invention and the robot coordinate system;

图4是本发明的全局坐标系与机械人坐标系的立体示意图；Fig. 4 is the three-dimensional schematic diagram of the global coordinate system of the present invention and the robot coordinate system;

图5是本发明的6轴机械人的立体图；5 is a perspective view of a 6-axis robot of the present invention;

图6是图4中6轴机械人各关节之间的位置关系示意图；Figure 6 is a schematic diagram of the positional relationship between the joints of the 6-axis robot in Figure 4;

图7是用于对整个协同系统的加工精度进行评价的标准模型的主视图。FIG. 7 is a front view of a standard model for evaluating the machining accuracy of the entire cooperative system.

具体实施方式Detailed ways

下述以三组加工机器人组成的协同加工系统对医疗产品进行加工为例为例，对本发明专利作出详细的说明。The following is an example of the processing of medical products by a collaborative processing system composed of three groups of processing robots to give a detailed description of the patent of the present invention.

机器人系统系统系统由三个不同功能的的机器人组成，每个机器人都有其特定的功能。 它们分别是切割机器人（CuR），冷却机器人（CoR）和夹持机器人（HoR）。 我们根据机器人的预期功能选择了三种不同型号的机器人。夹持机器人在夹持臂处的最大载荷为14kg，最大作用距离为820mm，以在加工过程中能够牢牢夹持医疗产品。切割机器人（CuR）加工刀具的机械臂的最大负载为12 kg，最长最大可达1441mm，并配有用于加工的铣削工具。 冷却机械手（CoR）机械臂的最大负载为7 kg，最大作用范围为717mm，可通过在机械臂上安装带有CO2冷却喷嘴的喷射装置。Robot System The system system consists of three robots with different functions, each robot has its specific function. They are Cutting Robot (CuR), Cooling Robot (CoR) and Holding Robot (HoR). We selected three different models of the robot based on the expected functionality of the robot. The maximum load of the gripping robot at the gripping arm is 14kg, and the maximum working distance is 820mm, so that the medical product can be firmly gripped during processing. The cutting robot (CuR) machining tool has a robotic arm with a maximum load of 12 kg, a maximum length of 1441 mm, and is equipped with a milling tool for machining. The cooling manipulator (CoR) manipulator has a maximum load of 7 kg and a maximum reach of 717mm, which can be achieved by installing a spray device with CO2 cooling nozzles on the manipulator.

如图1所示，以上三机器人安装在一个平面的刚性基座上。机器人之间以三角形排列布置，将待加工的医疗产品防止于刚性基座的质心位置。医疗产品以及每个机器人之间的径向距离可以沿径向方向进行微调，并基于以下标准和优先级：（1）将整个系统装置的重心与质心对齐以实现稳定性；（2）每个机器人的放置距离大约小于机器人的机械臂的一半，以使机械臂能够覆盖加工所需的工作半径，提供足够的伸展空间并最小化弯矩；（3）为每个机器人提供足够的间距，以避免/最大程度地减少机械臂的相互干涉。As shown in Figure 1, the above three robots are installed on a flat rigid base. The robots are arranged in a triangular arrangement to prevent the medical product to be processed at the center of mass of the rigid base. The medical product and the radial distance between each robot can be fine-tuned in the radial direction based on the following criteria and priorities: (1) align the center of gravity of the entire system setup with the center of mass for stability; (2) each The placement distance of the robot is about less than half of the robot arm, so that the robot arm can cover the working radius required for processing, provide enough stretch space and minimize the bending moment; (3) Provide enough spacing for each robot to Avoid/minimize the mutual interference of the robotic arms.

除了工作基座和三个机器人外，其他设备和附件（例如二氧化碳气体发生器，工具架等）都放置在便于取用的位置，同时避免干扰机械臂的路径。整个系统安装密闭式的加工仓中，并在加工仓内形成自上而下的对流以符合ISO14644 7级空气清洁度。With the exception of the work base and the three robots, other equipment and accessories (such as CO2 gas generators, tool holders, etc.) are placed for easy access while avoiding interfering with the path of the robotic arms. The whole system is installed in a closed processing chamber, and the top-down convection is formed in the processing chamber to meet the ISO14644 level 7 air cleanliness.

我们使用以上三机械人协同加工系统制造具有定制形状的金属距骨假体。距骨的外形与人类脚踝的相同。金属距骨首先通过增材制造产生出来。 增材制造的整个零件包括距骨零件和支撑柱，如图2所示。需要将所有支撑柱从金属距骨整个表面分离并对金属距骨进行表面处理达至要求的精度，才为完成距骨的制造。We use the above three-robot co-processing system to manufacture metal talus prostheses with custom shapes. The shape of the talus is the same as that of the human ankle. The metal talus was first produced by additive manufacturing. The additively manufactured entire part includes the talus part and the support column, as shown in Figure 2. To complete the manufacture of the talus, all support posts need to be separated from the entire surface of the metal talus and surface treated to the required precision.

在以上的制造过程中，加工顺序如下： 首先从采用切割机器完成平面铣削，目标是去除所有的支撑柱，然后对金属距骨的表面进行球磨，旨在获得定制形状的金属距骨轮廓，最后对金属距骨表面进行抛光，获得指定表面精度的距骨假体， 如图2所示。In the above manufacturing process, the machining sequence is as follows: First complete the face milling using a cutting machine, with the goal of removing all the support posts, then ball milling the surface of the metal talus, aiming to obtain a custom-shaped metal talus profile, and finally the metal talus. The surface of the talus was polished to obtain a talus prosthesis with a specified surface finish, as shown in Figure 2.

具体如何将机器人基座的基座坐标系与全域坐标系（即处理对象的坐标系）、机器人的内建坐标系与其基座的基座坐标系分别建立连接关系，下面作出详细说明。Specifically, how to establish the connection relationship between the base coordinate system of the robot base and the global coordinate system (that is, the coordinate system of the processing object), the built-in coordinate system of the robot and the base coordinate system of the base, respectively, is described in detail below.

首先，由处理对象的坐标系建立全域坐标系，可使用现有的产品设计软件，如AutoCAD, Mechanical等等，以AutoCAD为例，从CAD数据库中获取全域坐标WCS的坐标信息。WCS的坐标信息应包括以下四组信息。First, the global coordinate system is established from the coordinate system of the processing object. Existing product design software, such as AutoCAD, Mechanical, etc., can be used. Taking AutoCAD as an example, the coordinate information of the global coordinate WCS can be obtained from the CAD database. The coordinate information of WCS should include the following four groups of information.

i)WCS的原点坐标=（0,0,0）。i) Origin coordinates of WCS = (0,0,0).

ii)X主轴的单位矢量，WCS=[1, 0, 0]。ii) The unit vector of the X axis, WCS=[1, 0, 0].

iii) Y主轴的单位矢量，WCS=[0, 1, 0]。iii) Unit vector of the Y axis, WCS=[0, 1, 0].

iv)Z主轴的单位矢量WCS=[0, 0, 1]。iv) The unit vector WCS=[0, 0, 1] of the Z axis.

然后，从CAD数据库中获取每个机器人Z(i)的基座{(i,0)}与WCS相关的坐标信息。每个机器人基座{(i,0)}的所有坐标信息也包括以下四组信息。Then, the WCS-related coordinate information of the base {(i, 0)} of each robot Z(i) is obtained from the CAD database. All coordinate information of each robot base {(i,0)} also includes the following four sets of information.

i）每个机器人的基座{(i,0)}的原点在全局坐标中的坐标为Ri=(Xi,0, Yi,0,Zi,0)。i) The origin of the base {(i, 0)} of each robot has the coordinates Ri=(Xi, 0, Yi, 0, Zi, 0) in global coordinates.

ii）每个机器人的基座{(i,0)}的中其相对于基座坐标X主轴的矢量（[a,b,c]）映射到全局坐标的X轴的矢量为Ri =[aXi,0, bXi,0, cXi,0]。ii) The vector of each robot's base {(i,0)} where its vector ([a,b,c]) relative to the base coordinate X main axis maps to the X axis of the global coordinate is Ri = [aXi ,0,bXi,0,cXi,0].

iii) 每个机器人的基座{(i,0)}的中其相对于基座坐标Y主轴的矢量（[a,b,c]）映射到全局坐标的Y轴的矢量为Ri =[aYi,0, bYi,0, cYi,0]。iii) Each robot's base {(i,0)} where its vector ([a,b,c]) relative to the base coordinate Y-axis is mapped to the global coordinate's Y-axis as Ri = [aYi ,0,bYi,0,cYi,0].

iv)每个机器人的基座{(i,0)}的中其相对于基座坐标Z主轴的矢量（[a,b,c]）映射到全局坐标的Z轴的矢量为Ri =[aZi,0, bZi,0, cZi,0]。iv) The vector of the base {(i,0)} of each robot where its vector ([a,b,c]) relative to the base coordinate Z-axis is mapped to the Z-axis of the global coordinate is Ri = [aZi ,0,bZi,0,cZi,0].

其中如图3及4所示，表示了机器人内建坐标系与全局坐标系之间的位置关系。As shown in Figures 3 and 4, the positional relationship between the robot's built-in coordinate system and the global coordinate system is shown.

根据Denavit-Hartenburg转换，机器人的安装基座的基座坐标系与全域坐标系的位置关系建立以下其次变换方程：According to the Denavit-Hartenburg transformation, the positional relationship between the base coordinate system of the robot's installation base and the global coordinate system establishes the following transformation equation:

A_i,F=

……(3)A_i,F=

...(3)

接着，对协同加工系统的每个机器人建立运动模型。Next, a motion model is established for each robot of the collaborative processing system.

串接式机械人由一组链接成链并通过关节连接的机械臂组成。每个机器人假设都由M个机械臂组成，这些机械臂具有M_i自由度。首先，机械臂相对于其自身的坐标系进行建模，假设的每个机器人自身原点为（0,0），且该原点位于机器人的第一机械臂的输入关节处。A tandem robot consists of a set of robotic arms linked in a chain and connected by joints. Each robot is assumed to consist of M robotic arms with M_i degrees of freedom. First, the robotic arm is modeled relative to its own coordinate system, assuming that each robot's own origin is (0,0), and the origin is located at the input joint of the robot's first robotic arm.

那么运动方程的推导是基于i)德纳维特·哈特堡（D-H）公式以及ii）齐次转换。The derivation of the equations of motion is then based on i) the Denavit Hartburg (D-H) formula and ii) the homogeneous transformation.

基于D-H公式，获得了第i个机器人上的第j关节的齐次变换方程，Based on the D-H formula, the homogeneous transformation equation of the jth joint on the ith robot is obtained,

A_i,j= Rotz(θ_i,j)Tansz(d_i,j)Transx(a_i,j)Rotx(α_i,j)=A_i,j = Rotz(θ_i,j) Tansz(d_i,j )Transx(a_i,j )Rotx(α_i,j )=

……(1)

……(1)

从而获得安装于机械人i上加工器械的运动方程为：Thus, the equation of motion of the processing equipment installed on the robot i is obtained as:

……(2)

……(2)

将方程（1）代入方程（2），得到具有M个自由度的串接式机器人的运动方程，该机器人以其自有的坐标系为参考，结果如下方程（6）所示。机器人的最末节的机械臂M（安装工件或加工刀具的机械臂）相对于第一节的机械臂（与安装基座连接的机械臂）的齐次变换矩阵，如下Substituting equation (1) into equation (2), the motion equation of the tandem robot with M degrees of freedom is obtained, the robot takes its own coordinate system as a reference, and the result is shown in equation (6) below. The homogeneous transformation matrix of the robotic arm M of the last segment of the robot (the robotic arm that installs the workpiece or the machining tool) relative to the robotic arm of the first segment (the robotic arm connected to the mounting base) is as follows

4X4矩阵n为相对坐标系x轴对于参考坐标系的方向余弦。o矩阵为相对坐标系y轴对于参考坐标系的方向余弦。a矩阵为相对坐标系z轴对于参考坐标系的方向余弦。P为相对坐标系对于参考坐标系的位置向量。The 4X4 matrix n is the cosine of the direction of the x-axis of the relative coordinate system with respect to the reference coordinate system. The o matrix is the direction cosine of the y-axis of the relative coordinate system with respect to the reference coordinate system. The a matrix is the direction cosine of the z-axis of the relative coordinate system with respect to the reference coordinate system. P is the position vector of the relative coordinate system to the reference coordinate system.

以上已经建立了安装基座的基座坐标系与全域坐标系的位置关系的变换方程。但是每个机器人i是安装在器对应的安装基座I上，而且机器人i也通常也会内建坐标系，因此需要将机械人i的内建坐标系与安装基座I的基座坐标系的位置关系建立以下齐次变换方程：The transformation equation of the positional relationship between the base coordinate system of the installation base and the global coordinate system has been established above. However, each robot i is installed on the corresponding installation base I, and the robot i usually also has a built-in coordinate system, so it is necessary to connect the built-in coordinate system of the robot i with the base coordinate system of the installation base I The positional relationship of , establishes the following homogeneous transformation equation:

A_i,I=

……(4)A_i,I=

...(4)

上式中分别i，I为自然数，，

、

、

及

为安装基座I相对于全局坐标系的扭角、长度、偏移距离和夹角。In the above formula, i and I are natural numbers, respectively,

,

,

and

It is the torsion angle, length, offset distance and included angle of the mounting base I relative to the global coordinate system.

最后将于机械人i上加工器械的相对于全域坐标的运动方程为：Finally, the motion equation of the tool to be processed on robot i relative to the global coordinates is:

……(5)

...(5)

将上述运动方程应用于三机械人协同加工系统，并设定三个机器人都具有6个自由度。三个机器人均具有相同的配置。连杆和关节的布置，所有轴的原始位置如图5所示。其中6个自由度分别为J1，J2，J3，J4，J5和J6的六个旋转轴。这六个轴J1，J2，J3，J4，J5和J6的角运动记为θ1，θ2，θ3，θ4，θ5和θ6。在研究这三个机器人时，发明人注意到J4和J6的Z轴的旋转轴不是基于通常文献中使用的右手定则。为避免这两个轴J4和J6的符号约定不一致引起的问题，我们更改了J4和J6的符号方向。在这两个改变之后，角位移θi的符号约定所有轴均遵循右手定则。其余部分将使用“右手定则”。因此，θ4和θ6的方向与机器人制造商的方向是相反。J4和J6需要进行相应的转换。The above motion equation is applied to the three-robot collaborative processing system, and all three robots are set to have 6 degrees of freedom. All three robots have the same configuration. The arrangement of the links and joints, and the original positions of all axes are shown in Figure 5. The six degrees of freedom are the six rotational axes of J1, J2, J3, J4, J5 and J6, respectively. The angular motions of these six axes J1, J2, J3, J4, J5 and J6 are denoted as θ1, θ2, θ3, θ4, θ5 and θ6. While studying these three robots, the inventors noticed that the rotation axes of the Z-axis of J4 and J6 are not based on the right-hand rule commonly used in the literature. To avoid problems caused by inconsistent sign conventions for these two axes, J4 and J6, we changed the sign directions of J4 and J6. After these two changes, the sign convention for the angular displacement θi follows the right-hand rule for all axes. The rest will use the "Right Hand Rule". Therefore, the directions of θ4 and θ6 are opposite to those of the robot manufacturer. J4 and J6 need to be converted accordingly.

每个机器人的关节采用（R⊥R∥R⊥R⊥R⊥R）布置，如图6所示。The joints of each robot are arranged in (R⊥R∥R⊥R⊥R⊥R), as shown in Figure 6.

下列表格给出了导出运动模型所需的机器人D-H参数。The following table gives the robot D-H parameters required to derive the kinematic model.

表1 三个6自由度机器人的D-H参数Table 1 D-H parameters of three 6-DOF robots

表2 三个6自由度机器人的关节转动范围Table 2 Joint rotation range of three 6-DOF robots

表3 三个6自由度机器人的机械臂长度（ai）和机械臂偏移距离（di）Table 3 Arm length (ai) and arm offset distance (di) of three 6DOF robots

由上述方程（1）中的可以获得每个关节的变换矩阵。 将表1中的参数代入方程式（1），以找到每个变换矩阵。 在等式（4）中获得六个转换矩阵，如下所示： The transformation matrix of each joint can be obtained from the above equation (1). Substitute the parameters from Table 1 into equation (1) to find each transformation matrix. The six transformation matrices are obtained in equation (4) as follows:

……(7)

...(7)

将上述方程（5）中获得的六个轴的变换矩阵按方程（2）所示的顺序相乘，得到：Multiplying the transformation matrices of the six axes obtained in Equation (5) above in the order shown in Equation (2) gives:

……(8)

……(8)

对于三个自由度机器人的第六机械臂相对于第一个机械臂的齐次变换矩阵为4x4矩阵，如下For the homogeneous transformation matrix of the sixth arm of the three-degree-of-freedom robot relative to the first arm, the homogeneous transformation matrix is a 4x4 matrix, as follows

……(9)

……(9)

……(10)...(10)

……(11)...(11)

……(12)...(12)

……(13)...(13)

对于多机械任在切削中的性能以及加工精度，需要通过标准模型对整个协同系统的加工精度进行评价。标准模型由发明人设计，它由四个部分组成，即球体、圆柱体、参考圆柱体和基础块，如图7所示。For the performance and machining accuracy of the multi-machine tool in cutting, it is necessary to evaluate the machining accuracy of the entire collaborative system through the standard model. The standard model was designed by the inventor, and it consists of four parts, namely a sphere, a cylinder, a reference cylinder and a base block, as shown in Figure 7.

球体用于评估3D曲面在曲面铣削上的机械加工能力。Spheres are used to evaluate the machinability of 3D surfaces on surface milling.

圆柱体用于评估曲面铣削中2D曲面的机器人机械加工能力。Cylinders are used to evaluate robotic machining capabilities of 2D surfaces in surface milling.

基础块用于评估平面机器人的加工能力。The foundation blocks are used to evaluate the machining capabilities of planar robots.

参考圆柱体用作评估球体和圆柱体的方向和几何公差等机械加工能力的参考框架。The reference cylinder is used as a frame of reference for evaluating machining capabilities such as orientation and geometric tolerances of spheres and cylinders.

在此零件上进行了平面铣削和表面铣削，铣刀路径由MasterCAM生成。该标准模型由HoR握持并由CuR切割，机器人的定向运动和对零件的切割由RobotMaster产生。Face milling and face milling were performed on this part, and the milling tool paths were generated by MasterCAM. The standard model is held by the HoR and cut by the CuR, and the directional movement of the robot and the cutting of the part are produced by the RobotMaster.

多机器人系统系统完成标准模型加工后，将其交予CNAS认可的校准实验室进行测量。After the multi-robot system completes the standard model processing, it is sent to a CNAS-accredited calibration laboratory for measurement.

表4显示了从测试报告[8]获得的加工单元的性能。Table 4 shows the performance of the machining unit obtained from the test report [8].

表4 标准模型的测量结果Table 4 Measurement results of the standard model

由表4可以看出，多机器人协同系统在表面铣削的切削精度要优于平面铣削。 简而言之，这种多机械人协同系统更适合于自由曲面切割。 这些加工偏差主要是由于机器人协同系统加工过程中的抖动，由于机器人的结构复杂会导致其刚性不足，主轴，刀具，固定工件的夹具都会造成影响。It can be seen from Table 4 that the cutting accuracy of the multi-robot collaborative system in surface milling is better than that in plane milling. In short, this multi-robot collaborative system is more suitable for free-form surface cutting. These machining deviations are mainly due to the jitter in the machining process of the robot collaborative system. Due to the complex structure of the robot, its rigidity is insufficient, and the spindle, the tool, and the fixture for fixing the workpiece will all have an impact.

上述实施例是涉及利用多机械人协同系统制造医疗产品的范例。而该多机械人协同系统还可以应用于实施医疗手术，其与医疗产品的原理相似，可将医疗产品替换为人体的手术部位，然后通过设定不同的多机械人协同对不同的手术步骤实施相应的手术操作。The above-described embodiments are examples involving the manufacture of medical products using a multi-robot collaborative system. The multi-robot collaborative system can also be applied to perform medical operations. It is similar to the principle of medical products. The medical product can be replaced with the surgical site of the human body, and then different surgical steps can be performed by setting different multi-robot collaborations. corresponding surgical procedures.

Claims (9)

1. The multi-robot collaboration system is characterized in that: the robot comprises an object to be processed and a plurality of robots arranged around the object to be processed, wherein corresponding processing instruments are arranged on the robots; the processing object is provided with a reference, and the processing instrument performs motion modeling on the motion of the processing instrument by taking the reference as a global coordinate system, and specifically comprises the following steps:

a. the robot i has M_iA degree of freedom of movement; establishing the following homogeneous transformation equation by using a built-in coordinate system of the robot i and a j-th joint arranged on the robot i:

A_i,j= Rotz(θ_i,j)Tansz(d_i,j)Transx(a_i,j)Rotx(α_i,j)=

……(1)

in the above formula i, j and M_iIs a natural number, and is provided with a plurality of groups,

、

、

and

respectively indicating a torsion angle of the mechanical arm, a length of the mechanical arm, an offset distance of the mechanical arm and an included angle of the mechanical arm;

so as to obtain the motion equation of the processing instrument arranged on the robot i as follows:

……(2)

b. establishing a position relation between a base coordinate system of an installation base I of the robot I and a universe coordinate system, and performing the following secondary transformation equation:

A_i,F=

……(3)

in the above formula, i is a natural number, F is a certain joint in the robot i,

、

、

and

respectively the torsion angle, the length, the offset distance and the included angle of a certain joint F relative to a global coordinate system;

c. establishing the following homogeneous transformation equation according to the position relation between the built-in coordinate system of the robot i and the base coordinate system of the mounting base:

A_i,I=

……(4)

in the above formula, I and I are natural numbers respectively,

、

、

and

the torsion angle, the length, the offset distance and the included angle of the mounting base I relative to the global coordinate system are set;

d. the equation of motion of the treatment instrument relative to the global coordinates obtained on the robot i is:

……(5)

the multi-robot collaboration system as in claim 1, wherein: the processing object is arranged at the central position of the system, and the robot is arranged around the processing object by taking the processing object as the center.

2. The multi-robot collaboration system as in claim 1, wherein: the robot fixing device is characterized by also comprising a rigid base for mounting the robot, wherein a locking device for fixing the robot is arranged on the rigid base.

3. The multi-robot collaboration system of claim 3, wherein: the locking device comprises a rigid adjusting slide rail locked on the rigid base by a screw.

4. The multi-robot collaboration system as in claim 1, wherein: the robot further comprises a clamping robot for fixing a processing object, and the processing object is clamped and fixed on a clamping seat arranged on the robot.

5. The multi-robot cooperative system as claimed in claim 1, applied to a method for machining an irregular workpiece, wherein: the robot comprises a cutting robot, a workpiece clamping robot and a cooling robot, wherein an irregular workpiece to be machined is arranged on a fixed seat of the workpiece clamping robot, a cutter for machining the workpiece is arranged on the cutting robot, and the cooling robot is provided with a coolant spraying device for cooling the workpiece; firstly, setting a coordinate system of a workpiece as a global coordinate system, then establishing a corresponding motion equation according to a position relation between own coordinates of each robot and the global coordinate system, generating a processing tool path through a processing contour of the workpiece, calculating and obtaining the own processing path of each robot according to the processing tool path and the corresponding motion equation of each robot by each robot, and finishing all processing procedures of the workpiece to be processed by the corresponding robot to control a tool, a fixed seat clamping the workpiece and a coolant injection device respectively.

6. The multi-robot cooperative system as claimed in claim 6, applied to a method for machining an irregular workpiece, wherein: the reference of the workpiece is a reference column formed on the surface of the workpiece or a base through three-dimensional printing, and a coordinate system of the workpiece is set by the reference column.

7. The multi-robot cooperative system as claimed in claim 6, applied to a method for machining an irregular workpiece, wherein: the three-dimensional scanning device is further provided with a three-dimensional scanner, the three-dimensional scanner scans the workpiece to be machined in real time to obtain the measuring size of the workpiece to be machined, the measuring size is compared with machining contour data of the workpiece, and if the measuring size exceeds a set machining error, the cutting robot controls the cutter to machine the workpiece to be machined according to the machining error.

8. The multi-robot cooperative system as claimed in claim 6, applied to a method for machining an irregular workpiece, wherein: the method also comprises the following working steps of resetting the robot:

i. mounting a standard spherical calibration workpiece on a workpiece clamping robot, and mounting a probe for resetting calibration on a cutting robot;

the cutting robot drives the probe to contact with different positions of the spherical calibration workpiece, a plurality of contact point coordinates are obtained, and the spherical center coordinates of the spherical calibration workpiece are calculated through contact point coordinate fitting;

and iii, recording the sphere center coordinates and simplifying a global coordinate system with the sphere center coordinates as an origin and X, Y and Z as direction vectors.

9. The machining accuracy evaluation method of the multi-robot cooperative system according to claim 1, characterized in that: firstly, a standard model is established, the standard model comprises a sphere, a cylinder, a reference cylinder and a foundation block, the standard model is used as a workpiece and installed in a multi-robot cooperative system, the robot calculates a processing route of the robot according to a processing amount set by the standard model, a processing tool path and a corresponding motion equation to obtain a self-contained processing route of the robot, the sphere, the cylinder and the foundation block of the standard model are processed to obtain a processed standard model, finally, the size of the processed standard model is measured, and data obtained through measurement are compared with the processing amount set by the standard model to obtain the processing precision of the multi-robot cooperative system.

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